Polinômios Test Quiz!

Explanation
The correct answer is 2x + 3y. This is because in basketball, a player scores 2 points for each basket made from inside the three-point line (represented by 2x) and 3 points for each basket made from outside the three-point line (represented by 3y). Therefore, the total number of points scored by the player can be calculated by multiplying the number of 2-point baskets by 2 and the number of 3-point baskets by 3, and then adding these two values together.

Explanation
The polynomial 4x + 2y represents the number of wheels in the parking lot. This is because each car has 4 wheels and each motorcycle has 2 wheels. Therefore, multiplying the number of cars by 4 (4x) and the number of motorcycles by 2 (2y) will give us the total number of wheels in the parking lot.

Explanation
The degree of a polynomial is determined by the highest power of the variable in the polynomial. In this case, the highest power of the variable "x" is 3, which means the polynomial has a degree of 3. Therefore, the correct answer is "3º grau."

Explanation
The given question asks for the polynomial that represents the sum of two polynomials: x² - 9x + 5 and 3x² + 7x - 1. To find the sum, we add the corresponding terms of the two polynomials. The sum of the x² terms is 4x², the sum of the x terms is -2x, and the sum of the constant terms is 4. Therefore, the polynomial that represents the sum is 4x² - 2x + 4.

Explanation
The figure represents a rectangular garden. The area of a rectangle is calculated by multiplying its length by its width. In this case, the length is represented by x and the width is represented by y. Therefore, the polynomial that represents the total area of the garden is 7(x + y), as it represents the product of the length and width.

Explanation
The polynomial 4x + 8 represents the area of the colored figure because it is the only polynomial that includes both x and a constant term. The coefficient of x, 4, represents the length of one side of the figure, and the constant term, 8, represents the width of the figure. Therefore, when multiplied together, the polynomial 4x + 8 gives the area of the figure.

Explanation
The correct answer is 6x + 5(x - 3). This expression represents the amount of money spent by the six people at the restaurant. The term 6x represents the cost of the six plates of the day, and the term 5(x - 3) represents the cost of the five desserts, with each dessert being 3 reais less than the plate of the day. By multiplying the 5 by (x - 3), we are accounting for the fact that the cost of the desserts depends on the cost of the plates of the day.

Explanation
The area of a rectangle is given by the product of its length and width. In this case, the area is given by the expression x^2 + 6x + 8. To find the length and width of the rectangle, we need to factorize the expression. The factors of x^2 + 6x + 8 are (x + 2)(x + 4). Therefore, the length of the rectangle is x + 2 and the width is x + 4. Since the question asks for the measurement of the smaller side, the answer is x + 2.

Explanation
The correct answer is 4x - 1. To find the quotient of the given polynomial divided by 3x + 2, we can use polynomial long division. By dividing 12x^2 + 5x - 2 by 3x + 2, we get a quotient of 4x - 1.

Explanation
To find the value of 5A + 3B + 2C, we need to determine the values of A, B, and C. Since the division is exact, the quotient polynomial Ax^2 + Bx + C will have no remainder. By dividing 2x^3 - 7x^2 + 11x - 10 by x - 2, we find that A = 2, B = -3, and C = 4. Plugging these values into 5A + 3B + 2C, we get 5(2) + 3(-3) + 2(4) = 10 - 9 + 8 = 11. Therefore, the value of the expression is 11.